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Ratios, unit rates, and proportional relationships — SHSAT practice questions

On the SHSAT Mathematics section, Ratios, unit rates, and proportional relationships covers comparing two parts of a whole, finding how much work two machines do in the same span of time, and converting leftover length among kilometers, meters, and centimeters. A student must form equivalent ratios, use a given difference to find each part and the total, convert units before subtracting, and combine unit rates over a common interval. Questions are short word problems whose five answer choices are usually single totals; traps include mixed units, scaling only one side of a ratio, and adding rates that are not yet aligned.

  • Section: Mathematics 57 questions on the paper
  • 406 practice questions in the app

Sample questions

Question 1

Machine A packs 3 crates every 4 minutes. Machine B packs 5 crates every 6 minutes. If both machines work for 24 minutes, how many crates do they pack in all?

  1. A32
  2. B36
  3. C38
  4. D40
Show answer

Answer: C — 38

Machine A works for 24÷4=624\div4=6 groups of 4 minutes, so it packs 6⋅3=186\cdot3=18 crates. Machine B works for 24÷6=424\div6=4 groups of 6 minutes, so it packs 4⋅5=204\cdot5=20 crates. Together they pack 38 crates.

Question 2

The ratio of fiction books to nonfiction books donated to a library is 5:35:3. If 18 more fiction books than nonfiction books are donated, how many books are donated in all?

  1. A60
  2. B72
  3. C80
  4. D90
Show answer

Answer: B — 72

The difference of 2 ratio parts equals 18 books, so each part equals 9 books. The total is 5+3=85+3=8 parts, and 8⋅9=728\cdot9=72 books.

Question 3

A cable is 2.75 kilometers long. A section measuring 850 meters is removed. Each kilometer contains 1,0001{,}000 meters, and each meter contains 100 centimeters. How many centimeters of cable remain?

  1. A190 centimeters
  2. B1,9001{,}900 centimeters
  3. C190,000190{,}000 centimeters
  4. D360,000360{,}000 centimeters
Show answer

Answer: C — 190,000190{,}000 centimeters

The cable begins at 2.75×1,000=2,7502.75 \times 1{,}000 = 2{,}750 meters, so 2,750−850=1,9002{,}750 - 850 = 1{,}900 meters remain, or 190,000190{,}000 centimeters.

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